Disclaimer: this is purposefully obtuse.
Other effects in the game which explicitly state they kill you:
Shadows, succubi, massive damage, death saving throws, beholder death ray (notably not even their disintegration ray kills you), power word kill, vampires, mind flayers, night hags, drow inquisitors.
Clearly, if they intended for disintegration to kill you, they'd have said so. Since specific overrides general, and there is no general rule that disintegrated creatures are dead, I rest my case. QED.
Nothing in the spell says they don't. By contrast, Wild Shape
Also, a pile of dust doesn't have a stat block because it's an object. It's not even sentient. But if you really really want to play as a lifeless pile of dust, knock yourself out.
Spells do what they say they do. So "it doesn't say they don't" isn't a defense unless you think I could argue that Haste changes my Dex to 30.
The spell also doesn't say you become an object. Compare to True Polymorph!